void PrintVectorAll(
char *filename,
Vector *v)
{
amps_File file;
int g;
Grid *grid;
if ((file = amps_Fopen(filename, "w")) == NULL)
{
amps_Printf("Error: can't open output file %s\n", filename);
exit(1);
}
amps_Fprintf(file, "===================================================\n");
grid = VectorGrid(v);
for(g = 0; g < GridNumSubgrids(grid); g++)
{
amps_Fprintf(file, "Subvector Number: %d\n", g);
PrintSubvectorAll(file, VectorSubvector(v, g));
}
amps_Fprintf(file, "===================================================\n");
fflush(file);
amps_Fclose(file);
}
/*--------------------------------------------------------------------------
* InputPorosity
*--------------------------------------------------------------------------*/
void InputPorosity(
GeomSolid * geounit,
GrGeomSolid *gr_geounit,
Vector * field)
{
/*-----------------------------------------------------------------------
* Local variables
*-----------------------------------------------------------------------*/
PFModule *this_module = ThisPFModule;
PublicXtra *public_xtra = (PublicXtra*)PFModulePublicXtra(this_module);
InstanceXtra *instance_xtra = (InstanceXtra*)PFModuleInstanceXtra(this_module);
double field_value = (public_xtra->field_value);
Grid *grid = (instance_xtra->grid);
Subgrid *subgrid;
Subvector *field_sub;
double *fieldp;
int subgrid_loop;
int i, j, k;
int ix, iy, iz;
int nx, ny, nz;
int r;
int index;
(void)geounit;
/*-----------------------------------------------------------------------
* Assign constant values to field
*-----------------------------------------------------------------------*/
/* extra variables for reading from file */
Type3 * dummy3;
dummy3 = (Type3*)(public_xtra->data);
Vector *ic_values = dummy3->ic_values;
Subvector *ic_values_sub;
double *ic_values_dat;
for (subgrid_loop = 0; subgrid_loop < GridNumSubgrids(grid); subgrid_loop++)
{
subgrid = GridSubgrid(grid, subgrid_loop);
field_sub = VectorSubvector(field, subgrid_loop);
/* new subvector from file */
ic_values_sub = VectorSubvector(ic_values, subgrid_loop);
ix = SubgridIX(subgrid);
iy = SubgridIY(subgrid);
iz = SubgridIZ(subgrid);
nx = SubgridNX(subgrid);
ny = SubgridNY(subgrid);
nz = SubgridNZ(subgrid);
/* RDF: assume resolution is the same in all 3 directions */
r = SubgridRX(subgrid);
fieldp = SubvectorData(field_sub);
/* new subvector data to read from */
ic_values_dat = SubvectorData(ic_values_sub);
GrGeomInLoop(i, j, k, gr_geounit, r, ix, iy, iz, nx, ny, nz,
{
index = SubvectorEltIndex(field_sub, i, j, k);
/* now assign the value from file to field */
// fieldp[index] = field_value;
fieldp[index] = ic_values_dat[index];
});
}
void PGSRF(
GeomSolid * geounit,
GrGeomSolid *gr_geounit,
Vector * field,
RFCondData * cdata)
{
/*-----------------*
* Local variables *
*-----------------*/
PFModule *this_module = ThisPFModule;
PublicXtra *public_xtra = (PublicXtra*)PFModulePublicXtra(this_module);
InstanceXtra *instance_xtra = (InstanceXtra*)PFModuleInstanceXtra(this_module);
/* Input parameters (see PGSRFNewPublicXtra() below) */
double lambdaX = (public_xtra->lambdaX);
double lambdaY = (public_xtra->lambdaY);
double lambdaZ = (public_xtra->lambdaZ);
double mean = (public_xtra->mean);
double sigma = (public_xtra->sigma);
int dist_type = (public_xtra->dist_type);
double low_cutoff = (public_xtra->low_cutoff);
double high_cutoff = (public_xtra->high_cutoff);
int max_search_rad = (public_xtra->max_search_rad);
int max_npts = (public_xtra->max_npts);
int max_cpts = (public_xtra->max_cpts);
Vector *tmpRF = NULL;
/* Conditioning data */
int nc = (cdata->nc);
double *x = (cdata->x);
double *y = (cdata->y);
double *z = (cdata->z);
double *v = (cdata->v);
/* Grid parameters */
Grid *grid = (instance_xtra->grid);
Subgrid *subgrid;
Subvector *sub_field;
Subvector *sub_tmpRF;
int NX, NY, NZ;
/* Subgrid parameters */
int nx, ny, nz;
double dx, dy, dz;
int nx_v, ny_v, nz_v;
int nx_v2, ny_v2, nz_v2;
int nxG, nyG, nzG;
/* Counters, indices, flags */
int gridloop;
int i, j, k, n, m;
int ii, jj, kk;
int i2, j2, k2;
int imin, jmin, kmin;
int rpx, rpy, rpz;
int npts;
int index1, index2, index3;
/* Spatial variables */
double *fieldp;
double *tmpRFp;
int iLx, iLy, iLz; /* Correlation length in terms of grid points */
int iLxp1, iLyp1, iLzp1; /* One more than each of the above */
int nLx, nLy, nLz; /* Size of correlation neighborhood in grid pts. */
int iLxyz; /* iLxyz = iLx*iLy*iLz */
int nLxyz; /* nLxyz = nLx*nLy*nLz */
int ix, iy, iz;
int ref;
int ix2, iy2, iz2;
int i_search, j_search, k_search;
int ci_search, cj_search, ck_search;
double X0, Y0, Z0;
/* Variables used in kriging algorithm */
double cmean, csigma; /* Conditional mean and std. dev. from kriging */
double A;
double *A_sub; /* Sub-covariance matrix for external cond pts */
double *A11; /* Submatrix; note that A11 is 1-dim */
double **A12, **A21, **A22;/* Submatrices for external conditioning data */
double **M; /* Used as a temporary matrix */
double *b; /* Covariance vector for conditioning points */
double *b_tmp, *b2;
double *w, *w_tmp; /* Solution vector to Aw=b */
int *ixx, *iyy, *izz;
double *value;
int di, dj, dk;
double uni, gau;
double ***cov;
int ierr;
/* Conditioning data variables */
int cpts; /* N cond pts for a single simulated node */
double *cval; /* Values for cond data for single node */
/* Communications */
VectorUpdateCommHandle *handle;
int update_mode;
/* Miscellaneous variables */
int **rand_path;
char ***marker;
int p, r, modulus;
double a1, a2, a3;
double cx, cy, cz;
double sum;
// FIXME Shouldn't we get this from numeric_limits?
double Tiny = 1.0e-12;
(void)geounit;
/*-----------------------------------------------------------------------
* Allocate temp vectors
*-----------------------------------------------------------------------*/
tmpRF = NewVectorType(instance_xtra->grid, 1, max_search_rad, vector_cell_centered);
/*-----------------------------------------------------------------------
* Start sequential Gaussian simulator algorithm
*-----------------------------------------------------------------------*/
/* Begin timing */
BeginTiming(public_xtra->time_index);
/* initialize random number generators */
SeedRand(public_xtra->seed);
/* For now, we will assume that all subgrids have the same uniform spacing */
subgrid = GridSubgrid(grid, 0);
dx = SubgridDX(subgrid);
dy = SubgridDY(subgrid);
dz = SubgridDZ(subgrid);
/* Size of search neighborhood through which random path must be defined */
iLx = (int)(lambdaX / dx);
iLy = (int)(lambdaY / dy);
iLz = (int)(lambdaZ / dz);
/* For computational efficiency, we'll limit the
* size of the search neighborhood. */
if (iLx > max_search_rad)
iLx = max_search_rad;
if (iLy > max_search_rad)
iLy = max_search_rad;
if (iLz > max_search_rad)
iLz = max_search_rad;
iLxp1 = iLx + 1;
iLyp1 = iLy + 1;
iLzp1 = iLz + 1;
iLxyz = iLxp1 * iLyp1 * iLzp1;
/* Define the size of a correlation neighborhood */
nLx = 2 * iLx + 1;
nLy = 2 * iLy + 1;
nLz = 2 * iLz + 1;
nLxyz = nLx * nLy * nLz;
/*------------------------
* Define a random path through the points in this subgrid.
* The random path generation procedure of Srivastava and
* Gomez has been adopted in this subroutine. A linear
* congruential generator of the form: r(i) = 5*r(i-1)+1 mod(2**n)
* has a cycle length of 2**n. By choosing the smallest power of
* 2 that is still larger than the total number of points to be
* simulated, the method ensures that all indices will be
* generated once and only once.
*------------------------*/
rand_path = talloc(int*, iLxyz);
for (i = 0; i < iLxyz; i++)
rand_path[i] = talloc(int, 3);
modulus = 2;
while (modulus < iLxyz + 1)
modulus *= 2;
/* Compute a random starting node */
p = (int)Rand();
r = 1 + p * (iLxyz - 1);
k = (r - 1) / (iLxp1 * iLyp1);
j = (r - 1 - iLxp1 * iLyp1 * k) / iLxp1;
i = (r - 1) - (k * iLyp1 + j) * iLxp1;
rand_path[0][2] = k;
rand_path[0][1] = j;
rand_path[0][0] = i;
/* Determine the next nodes */
for (n = 1; n < iLxyz; n++)
{
r = (5 * r + 1) % modulus;
while ((r < 1) || (r > iLxyz))
r = (5 * r + 1) % modulus;
k = ((r - 1) / (iLxp1 * iLyp1));
j = (((r - 1) - iLxp1 * iLyp1 * k) / iLxp1);
i = (r - 1) - (k * iLyp1 + j) * iLxp1;
rand_path[n][0] = i;
rand_path[n][1] = j;
rand_path[n][2] = k;
}
/*-----------------------------------------------------------------------
* Compute correlation lookup table
*-----------------------------------------------------------------------*/
/* First compute a covariance lookup table */
cov = talloc(double**, nLx);
for (i = 0; i < nLx; i++)
{
cov[i] = talloc(double*, nLy);
for (j = 0; j < nLy; j++)
cov[i][j] = ctalloc(double, nLz);
}
/* Note that in the construction of the covariance matrix
* the max_search_rad is not used. Covariance depends upon
* the correlation lengths, lambdaX/Y/Z, and the grid spacing.
* The max_search_rad can be longer or shorter than the correlation
* lengths. The bigger the search radius, the more accurately
* the random field will match the correlation structure of the
* covariance function. But the run time will increase greatly
* as max_search_rad gets bigger because of the kriging matrix
* that must be solved (see below).
*/
cx = 0.0;
cy = 0.0;
cz = 0.0;
if (lambdaX != 0.0)
cx = dx * dx / (lambdaX * lambdaX);
if (lambdaY != 0.0)
cy = dy * dy / (lambdaY * lambdaY);
if (lambdaZ != 0.0)
cz = dz * dz / (lambdaZ * lambdaZ);
for (k = 0; k < nLz; k++)
for (j = 0; j < nLy; j++)
for (i = 0; i < nLx; i++)
{
a1 = i * i * cx;
a2 = j * j * cy;
a3 = k * k * cz;
cov[i][j][k] = exp(-sqrt(a1 + a2 + a3));
}
/* Allocate memory for variables that will be used in kriging */
A11 = ctalloc(double, nLxyz * nLxyz);
A_sub = ctalloc(double, nLxyz * nLxyz);
A12 = ctalloc(double*, nLxyz);
A21 = ctalloc(double*, nLxyz);
A22 = ctalloc(double*, nLxyz);
M = ctalloc(double*, nLxyz);
for (i = 0; i < nLxyz; i++)
{
A12[i] = ctalloc(double, nLxyz);
A21[i] = ctalloc(double, nLxyz);
A22[i] = ctalloc(double, nLxyz);
M[i] = ctalloc(double, nLxyz);
}
b = ctalloc(double, nLxyz);
b2 = ctalloc(double, nLxyz);
b_tmp = ctalloc(double, nLxyz);
w = ctalloc(double, nLxyz);
w_tmp = ctalloc(double, nLxyz);
value = ctalloc(double, nLxyz);
cval = ctalloc(double, nLxyz);
ixx = ctalloc(int, nLxyz);
iyy = ctalloc(int, nLxyz);
izz = ctalloc(int, nLxyz);
/* Allocate space for the "marker" used to keep track of which
* points in a representative correlation box have been simulated
* already.
*/
marker = talloc(char**, (3 * iLx + 1));
marker += iLx;
for (i = -iLx; i <= 2 * iLx; i++)
{
marker[i] = talloc(char*, (3 * iLy + 1));
marker[i] += iLy;
for (j = -iLy; j <= 2 * iLy; j++)
{
marker[i][j] = ctalloc(char, (3 * iLz + 1));
marker[i][j] += iLz;
for (k = -iLz; k <= 2 * iLz; k++)
marker[i][j][k] = 0;
}
}
/* Convert the cutoff values to a gaussian if they're lognormal on input */
if ((dist_type == 1) || (dist_type == 3))
{
if (low_cutoff <= 0.0)
{
low_cutoff = Tiny;
}
else
{
low_cutoff = (log(low_cutoff / mean)) / sigma;
}
if (high_cutoff <= 0.0)
{
high_cutoff = DBL_MAX;
}
else
{
high_cutoff = (log(high_cutoff / mean)) / sigma;
}
}
/*--------------------------------------------------------------------
* Start pGs algorithm
*--------------------------------------------------------------------*/
for (gridloop = 0; gridloop < GridNumSubgrids(grid); gridloop++)
{
subgrid = GridSubgrid(grid, gridloop);
sub_tmpRF = VectorSubvector(tmpRF, gridloop);
sub_field = VectorSubvector(field, gridloop);
tmpRFp = SubvectorData(sub_tmpRF);
fieldp = SubvectorData(sub_field);
X0 = RealSpaceX(0, SubgridRX(subgrid));
Y0 = RealSpaceY(0, SubgridRY(subgrid));
Z0 = RealSpaceZ(0, SubgridRZ(subgrid));
ix = SubgridIX(subgrid);
iy = SubgridIY(subgrid);
iz = SubgridIZ(subgrid);
nx = SubgridNX(subgrid);
ny = SubgridNY(subgrid);
nz = SubgridNZ(subgrid);
NX = ix + nx;
NY = iy + ny;
NZ = iz + nz;
/* RDF: assume resolution is the same in all 3 directions */
ref = SubgridRX(subgrid);
nx_v = SubvectorNX(sub_field);
ny_v = SubvectorNY(sub_field);
nz_v = SubvectorNZ(sub_field);
nx_v2 = SubvectorNX(sub_tmpRF);
ny_v2 = SubvectorNY(sub_tmpRF);
nz_v2 = SubvectorNZ(sub_tmpRF);
/* Initialize tmpRF vector */
GrGeomInLoop(i, j, k, gr_geounit, ref, ix, iy, iz, nx, ny, nz,
{
index2 = SubvectorEltIndex(sub_tmpRF, i, j, k);
tmpRFp[index2] = 0.0;
});
/* Convert conditioning data to N(0,1) distribution if
* it's assumed to be lognormal. Then copy it into tmpRFp */
if ((dist_type == 1) || (dist_type == 3))
{
for (n = 0; n < nc; n++)
{
i = (int)((x[n] - X0) / dx + 0.5);
j = (int)((y[n] - Y0) / dy + 0.5);
k = (int)((z[n] - Z0) / dz + 0.5);
if ((ix - max_search_rad <= i && i <= ix + nx + max_search_rad) &&
(iy - max_search_rad <= j && j <= iy + ny + max_search_rad) &&
(iz - max_search_rad <= k && k <= iz + nz + max_search_rad))
{
index2 = SubvectorEltIndex(sub_tmpRF, i, j, k);
if (v[n] <= 0.0)
tmpRFp[index2] = Tiny;
else
tmpRFp[index2] = (log(v[n] / mean)) / sigma;
}
}
}
/* Otherwise, shift data to N(0,1) distribution */
else
{
for (n = 0; n < nc; n++)
{
i = (int)((x[n] - X0) / dx + 0.5);
j = (int)((y[n] - Y0) / dy + 0.5);
k = (int)((z[n] - Z0) / dz + 0.5);
if ((ix - max_search_rad <= i && i <= ix + nx + max_search_rad) &&
(iy - max_search_rad <= j && j <= iy + ny + max_search_rad) &&
(iz - max_search_rad <= k && k <= iz + nz + max_search_rad))
{
index2 = SubvectorEltIndex(sub_tmpRF, i, j, k);
tmpRFp[index2] = (v[n] - mean) / sigma;
}
}
}
/* Set the search radii in each direction. If the maximum
* number of points in a neighborhood is exceeded, these limits
* will be reduced. */
i_search = iLx;
j_search = iLy;
k_search = iLz;
/* Compute values at all points using all templates */
for (n = 0; n < iLxyz; n++)
{
/* Update the ghost layer before proceeding */
if (n > 0)
{
/* First reset max_search_radius */
max_search_rad = i_search;
if (j_search > max_search_rad)
max_search_rad = j_search;
if (k_search > max_search_rad)
max_search_rad = k_search;
/* Reset the comm package based on the new max_search_radius */
if (max_search_rad == 1)
update_mode = VectorUpdatePGS1;
else if (max_search_rad == 2)
update_mode = VectorUpdatePGS2;
else if (max_search_rad == 3)
update_mode = VectorUpdatePGS3;
else
update_mode = VectorUpdatePGS4;
handle = InitVectorUpdate(tmpRF, update_mode);
FinalizeVectorUpdate(handle);
}
rpx = rand_path[n][0];
rpy = rand_path[n][1];
rpz = rand_path[n][2];
ix2 = rpx; while (ix2 < ix)
ix2 += iLxp1;
iy2 = rpy; while (iy2 < iy)
iy2 += iLyp1;
iz2 = rpz; while (iz2 < iz)
iz2 += iLzp1;
/* This if clause checks to see if there are, in fact,
* any points at all in this subgrid, for this
* particular region. Note that each value of n in the
* above n-loop corresponds to a different region. */
if ((ix2 < ix + nx) && (iy2 < iy + ny) && (iz2 < iz + nz))
{
/*
* Construct the input matrix and vector for kriging,
* solve the linear system, and compute csigma.
* These depend only on the spatial distribution of
* conditioning data, not on the actual values of
* the data. Only the conditional mean (cmean) depends
* on actual values, so it must be computed for every
* point. Thus, it's found within the pgs_Boxloop below.
* The size of the linear system that must be solved here
* will be no larger than (2r+1)^3, where r=max_search_rad.
* It is clear from this why it is necessary to limit
* the size of the search radius.
*/
/* Here the marker array indicates which points within
* the search radius have been simulated already. This
* spatial pattern of conditioning points will be the
* same for every point in the current template. Thus,
* this system can be solved once *outside* of the
* GrGeomInLoop2 below. */
npts = 9999;
while (npts > max_npts)
{
m = 0;
/* Count the number of points in search ellipse */
for (k = rpz - k_search; k <= rpz + k_search; k++)
for (j = rpy - j_search; j <= rpy + j_search; j++)
for (i = rpx - i_search; i <= rpx + i_search; i++)
{
if (marker[i][j][k])
{
ixx[m] = i;
iyy[m] = j;
izz[m++] = k;
}
}
npts = m;
/* If npts is too large, reduce the size of the
* search ellipse one axis at a time. */
if (npts > max_npts)
{
/* If i_search is the biggest, reduce it by one. */
if ((i_search >= j_search) && (i_search >= k_search))
{
i_search--;
}
/* Or, if j_search is the biggest, reduce it by one. */
else if ((j_search >= i_search) && (j_search >= k_search))
{
j_search--;
}
/* Otherwise, reduce k_search by one. */
else
{
k_search--;
}
}
}
m = 0;
for (j = 0; j < npts; j++)
{
di = abs(rpx - ixx[j]);
dj = abs(rpy - iyy[j]);
dk = abs(rpz - izz[j]);
b[j] = cov[di][dj][dk];
for (i = 0; i < npts; i++)
{
di = abs(ixx[i] - ixx[j]);
dj = abs(iyy[i] - iyy[j]);
dk = abs(izz[i] - izz[j]);
A11[m++] = cov[di][dj][dk];
}
}
/* Solve the linear system */
for (i = 0; i < npts; i++)
w[i] = b[i];
if (npts > 0)
{
dpofa_(A11, &npts, &npts, &ierr);
dposl_(A11, &npts, &npts, w);
}
/* Compute the conditional standard deviation for the RV
* to be simulated. */
csigma = 0.0;
for (i = 0; i < npts; i++)
csigma += w[i] * b[i];
csigma = sqrt(cov[0][0][0] - csigma);
/* The following loop hits every point in the current
* region. That is, it skips by max_search_rad+1
* through the subgrid. In this way, all the points
* in this loop may simulated simultaneously; each is
* outside the search radius of all the others. */
nxG = (nx + ix);
nyG = (ny + iy);
nzG = (nz + iz);
for (k = iz2; k < nzG; k += iLzp1)
for (j = iy2; j < nyG; j += iLyp1)
for (i = ix2; i < nxG; i += iLxp1)
{
index1 = SubvectorEltIndex(sub_field, i, j, k);
index2 = SubvectorEltIndex(sub_tmpRF, i, j, k);
/* Only simulate points in this geounit and that don't
* already have a value. If a node already has a value,
* it was assigned as external conditioning data,
* so we don't need to simulate it. */
if (fabs(tmpRFp[index2]) < Tiny)
{
/* Condition the random variable */
m = 0;
cpts = 0;
for (kk = -k_search; kk <= k_search; kk++)
for (jj = -j_search; jj <= j_search; jj++)
for (ii = -i_search; ii <= i_search; ii++)
{
value[m] = 0.0;
index3 = SubvectorEltIndex(sub_tmpRF, i + ii, j + jj, k + kk);
if (marker[ii + rpx][jj + rpy][kk + rpz])
{
value[m++] = tmpRFp[index3];
}
/* In this case, there is a value at this point,
* but it wasn't simulated yet (as indicated by the
* fact that the marker has no place for it). Thus,
* it must be external conditioning data. */
else if (fabs(tmpRFp[index3]) > Tiny)
{
ixx[npts + cpts] = rpx + ii;
iyy[npts + cpts] = rpy + jj;
izz[npts + cpts] = rpz + kk;
cval[cpts++] = tmpRFp[index3];
}
}
/* If cpts is too large, reduce the size of the
* search neighborhood, one axis at a time. */
/* Define the size of the search neighborhood */
ci_search = i_search;
cj_search = j_search;
ck_search = k_search;
while (cpts > max_cpts)
{
/* If ci_search is the biggest, reduce it by one. */
if ((ci_search >= cj_search) && (ci_search >= ck_search))
ci_search--;
/* Or, if cj_search is the biggest, reduce it by one. */
else if ((cj_search >= ci_search) && (cj_search >= ck_search))
cj_search--;
/* Otherwise, reduce ck_search by one. */
else
ck_search--;
/* Now recount the conditioning data points */
m = 0;
cpts = 0;
for (kk = -ck_search; kk <= ck_search; kk++)
for (jj = -cj_search; jj <= cj_search; jj++)
for (ii = -ci_search; ii <= ci_search; ii++)
{
index3 = SubvectorEltIndex(sub_tmpRF, i + ii, j + jj, k + kk);
if (!(marker[rpx + ii][rpy + jj][rpz + kk]) &&
(fabs(tmpRFp[index3]) > Tiny))
{
ixx[npts + cpts] = rpx + ii;
iyy[npts + cpts] = rpy + jj;
izz[npts + cpts] = rpz + kk;
cval[cpts++] = tmpRFp[index3];
}
}
}
for (i2 = 0; i2 < npts; i2++)
w_tmp[i2] = w[i2];
/*--------------------------------------------------
* Conditioning to external data is done here.
*--------------------------------------------------*/
if (cpts > 0)
{
/* Compute the submatrices */
for (j2 = 0; j2 < npts + cpts; j2++)
{
di = abs(rpx - ixx[j2]);
dj = abs(rpy - iyy[j2]);
dk = abs(rpz - izz[j2]);
b[j2] = cov[di][dj][dk];
for (i2 = 0; i2 < npts + cpts; i2++)
{
di = abs(ixx[i2] - ixx[j2]);
dj = abs(iyy[i2] - iyy[j2]);
dk = abs(izz[i2] - izz[j2]);
A = cov[di][dj][dk];
if (i2 < npts && j2 >= npts)
A12[i2][j2 - npts] = A;
if (i2 >= npts && j2 < npts)
A21[i2 - npts][j2] = A;
if (i2 >= npts && j2 >= npts)
A22[i2 - npts][j2 - npts] = A;
}
}
/* Compute b2' = b2 - A21 * A11_inv * b1 and augment b1 */
for (i2 = 0; i2 < cpts; i2++)
b2[i2] = b[i2 + npts];
for (i2 = 0; i2 < npts; i2++)
b_tmp[i2] = b[i2];
dposl_(A11, &npts, &npts, b_tmp);
for (i2 = 0; i2 < cpts; i2++)
{
sum = 0.0;
for (j2 = 0; j2 < npts; j2++)
{
sum += A21[i2][j2] * b_tmp[j2];
}
b2[i2] -= sum;
}
for (i2 = 0; i2 < cpts; i2++)
b[i2 + npts] = b2[i2];
/* Compute A22' = A22 - A21 * A11_inv * A12 */
for (j2 = 0; j2 < cpts; j2++)
for (i2 = 0; i2 < npts; i2++)
M[j2][i2] = A12[i2][j2];
if (npts > 0)
{
for (i2 = 0; i2 < cpts; i2++)
dposl_(A11, &npts, &npts, M[i2]);
}
for (j2 = 0; j2 < cpts; j2++)
for (i2 = 0; i2 < cpts; i2++)
{
sum = 0.0;
for (k2 = 0; k2 < npts; k2++)
sum += A21[i2][k2] * M[j2][k2];
A22[i2][j2] -= sum;
}
m = 0;
for (j2 = 0; j2 < cpts; j2++)
for (i2 = 0; i2 < cpts; i2++)
A_sub[m++] = A22[i2][j2];
/* Compute x2 where A22*x2 = b2' */
dpofa_(A_sub, &cpts, &cpts, &ierr);
dposl_(A_sub, &cpts, &cpts, b2);
/* Compute w_tmp where A11*w_tmp = (b1 - A12*b2) */
if (npts > 0)
{
for (i2 = 0; i2 < npts; i2++)
{
sum = 0.0;
for (k2 = 0; k2 < cpts; k2++)
sum += A12[i2][k2] * b2[k2];
w_tmp[i2] = b[i2] - sum;
}
dposl_(A11, &npts, &npts, w_tmp);
}
/* Fill in the rest of w_tmp with b2 */
for (i2 = npts; i2 < npts + cpts; i2++)
{
w_tmp[i2] = b2[i2];
value[i2] = cval[i2 - npts];
}
/* Recompute csigma */
csigma = 0.0;
for (i2 = 0; i2 < npts + cpts; i2++)
csigma += w_tmp[i2] * b[i2];
csigma = sqrt(cov[0][0][0] - csigma);
}
/*--------------------------------------------------
* End of external conditioning
*--------------------------------------------------*/
cmean = 0.0;
for (m = 0; m < npts + cpts; m++)
cmean += w_tmp[m] * value[m];
/* uni = fieldp[index1]; */
uni = Rand();
gauinv_(&uni, &gau, &ierr);
tmpRFp[index2] = csigma * gau + cmean;
/* Cutoff tail values if required */
if (dist_type > 1)
{
if (tmpRFp[index2] < low_cutoff)
tmpRFp[index2] = low_cutoff;
if (tmpRFp[index2] > high_cutoff)
tmpRFp[index2] = high_cutoff;
}
} /* if( abs(tmpRFp[index2]) < Tiny ) */
}
/* end of triple for-loops over i,j,k */
/* Update the marker vector */
imin = rpx - iLxp1; if (imin < -iLx)
imin += iLxp1;
jmin = rpy - iLyp1; if (jmin < -iLy)
jmin += iLyp1;
kmin = rpz - iLzp1; if (kmin < -iLz)
kmin += iLzp1;
for (kk = kmin; kk <= 2 * iLz; kk += iLzp1)
for (jj = jmin; jj <= 2 * iLy; jj += iLyp1)
for (ii = imin; ii <= 2 * iLx; ii += iLxp1)
{
marker[ii][jj][kk] = 1;
}
} /* if(...) */
} /* n loop */
/* Make log-normal if requested. Note that low
* and high cutoffs are already accomplished. */
if ((dist_type == 1) || (dist_type == 3))
{
GrGeomInLoop(i, j, k, gr_geounit, ref, ix, iy, iz, nx, ny, nz,
{
index1 = SubvectorEltIndex(sub_field, i, j, k);
index2 = SubvectorEltIndex(sub_tmpRF, i, j, k);
fieldp[index1] = mean * exp((sigma) * tmpRFp[index2]);
});